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Using ANFIS and Fuzzy Clustering to Predict
Extreme Climate in Indonesian regions
The Houw Liong
2)
and Plato M.Siregar
1)
ICICI 2007 proceedingsJl. Ganesha 10
Bandung, 40132 INA1) Faculty of Earth Science and Mineral Technology, ITB2) Faculty of Mathematics and Natural Sciences, ITB
Abstract
Extreme climate in Indonesia is influenced by four
main quasi periodic cycles: Solar Activity Cycle (Sunspot
Numbers Cycle), Galactic Cosmic Ray Cycle, El Nino
Southern Oscillation (ENSO) Cycle, and Indian Ocean Dipole
Mode (IOD) Cycle. It can be shown that solar activity cycle
can be considered as primary cycle that influence other cycles.
In practice eastern Indonesian region is dominantly
influenced by ENSO. When the heat pools moves to eastern
Indonesian region, then rainfall in this region will be above
normal. On the other hand when the heat pool leaves eastern
Indonesian region and moves to Pacific Ocean then the rainfall
in this region will be below normal.
During a typical Indian Ocean Dipole Mode (IOD)event the weakening and reversal of winds in the central
equatorial Indian Ocean lead to the development of unusually
warm sea surface temperatures in the western Indian Ocean.
IOD negative means wet condition or the rainfall will be above
normal along the western Indonesian region.
Precipitation in Pontianak region which represent
middle Indonesian region correlated strongly with sunspotnumbers cycle (solar activity cycle).
Using ANFIS (Adaptive Neuro Fuzzy Inference System)
we are able to predict sunspot numbers cycles so that extreme
weather in Indonesian regions can be predicted.
Fuzzy c-means is used to classify regions that are
influenced strongly by sunspot numbers (solar activity), IOD,and ENSO cycles. This method is based on fuzzy set as fuzzyc-partition of three cycles above and as clustercenter. Fuzzy c-
partition matrix for grouping a collection of n data set into c
classes.
This study explores the physical of climate predictions
and classifications of Indonesian regions and its physical
interpretations.
Keywords: ANFIS, fuzzy clustering, climate, solar activity
I. INTRODUCTION
The relative positions of the sun in the sky during the
seasons, as well as the cycles of solar activity influence the
weather and climate throughout the Indonesian archipelago.
Solar irradiance and ultraviolet intensity increases with higher
solar activity. This in turn will be followed by coronal mass
ejection (CME) that increases the charged particles emitted by
the sun which could alter the interplanetary magnetic field, and
hence the intensity of galactic cosmic rays reaching the earth.
The galactic cosmic ray intensity reaching the earth decreases
with higher solar activity. Thus the solar activity is often
considered as the dominant factor that determines the dynamics
of climate [1, 2]. The dynamics of earth's atmosphere and
oceans, evaporation, clouds formation and rainfall, are
influenced by the solar energy entering the earth. Several
studies indicate that strong correlations exist between the cloud
cover and the intensity of galactic cosmic ray reaching the
earth [3].
During 1645 1715 exceptionally low solar activity
(also known as the Maunder minimum) which means high
intensity of galactic cosmic ray reached the earth increased
cloud cover that led to low temperatures causing what is known
as the little ice age.
The present study shows that there is a strong correlation
between rainfall in the Indonesian archipelago and solar
activity or sunspot numbers.
II. THE RELATION BETWEEN SOLAR ACTIVITY
AND CLIMATEThe galactic cosmic rays collide with air molecules in
the upper atmosphere and produce secondary particles.
Generally the charged particles so produced cannot penetrate to
lower layers of the atmosphere, except gamma ray, neutrons
and the muons. When gamma ray, neutrons and muons interact
with the air molecules or water molecules, they become
charged and together with aerosols particles act as
condensation nuclei for the formation of clouds. The cosmic
ray becomes the source of ions in the air besides radiation
coming from earth originated by the radio isotope radon.
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During the sunspot minimum, the intensity of the
galactic cosmic ray that penetrates earth atmosphere becomes
maximum which in turn increases the coverage of clouds. This
implies that solar irradiation reaching the earth will be
minimized. Conversely, during solar activity maximum or
sunspot maximum, the intensity of galactic cosmic ray
reaching lower levels of the atmosphere decreases, less cloud
condensation nuclei are produced, hence the cloud cover
decreases, furthermore extra energy received from flares during
prominent eruptions, maximizes the amount of solar energy
reaches the earth.
Although global cloud cover produces a warming effect
or the greenhouse effect, but a cooling effect due to reflections
against direct solar irradiation is more dominant factor [1, 3].
Furthermore during solar activity maximum, the
intensity of ultraviolet that penetrates the earth increases. Solar
activity maximum usually is followed by increasing coronal
mass ejection. Both effects caused greater amount of energy
penetrates the earth and this will influence the climate through
the dynamics of the atmosphere and oceans.
III. Adaptive Neuro-Fuzzy Inference System (ANFIS)
and Fuzzy Clustering
Adaptive network-based fuzzy inference system used a
feed forward network to search for fuzzy decision rules that
perform well on a given task. Using a given input-output data
set ANFIS creates a fuzzy inference system whose
membership function parameters are adjusted using a
backpropagation algorithm alone or combination between abackpropagation algorithm with a least squares method. This
allows the fuzzy systems to learn from the data being modeled.
ANFIS provide a method for the fuzzy modeling procedure to
learn information from the data set, followed by creating the
membership function parameters that best performing the given
task. Consider a first order Takagi-Sugeno fuzzy model with a
two input, one output system having two membership functions
for each input.[6]
The functioning of ANFIS is a five layered feed forward neural
structure and the functionality of the nodes in these layers can
be summarized as follows:Layer 1: Every node i in this layer is an adaptive node with a
node output defined by:
(1)
wherex(ory) is the input to the node; Ai (orBi-2) is a fuzzy set
associated with this node, characterized by the shape of the
membership function in this node and can be any appropriate
functions that are continuous and piecewise differentiable such
as Gaussian , generalized bell shaped, trapezoidal shaped and
triangular shaped functions. Assuming a bell shaped function
as the membership function,Ai can be computed as,
(2)
ai and ci are the parameter set. Parameters in this layer are
referred to as premise (antecedent) parameters.
Layer 2: Every node in this layer is a fixed node labeled ,
which multiplies the incoming signals and outputs the product.
For instance,
(3)
Each node output represents the firing strength of a rule.
Layer 3: Every node in this layer is a circle node labeledN. The
ith node calculates the ratio of the ith rule's firing strength to
the sum of all rule's firing strengths. Output of this layer will be
called normalized firing strengths.
(4)
Layer 4: Node i in this layer compute the contribution of the ith
rule towards the model output, with the following node
functions:
(5)
Layer 5: The single node in this layer is a fixed node labeled
that computes the overall output as the summation of all
incoming signals.
Overall output =
(6)
Using ANFIS and data from Royal Observatory of Belgium
and Sunspot Index Data Centerhttp://www.astro.oma.be/SIDC
we can get prediction of sunspot numbers time series as in
Figure 1.
b2
i
i
A
a
cx1
1
)x( +
=
2,1i)y()x(wO ii BA1i,2 ===
2,1i,ww
wwO
21
iii,3 =
+
==
)ryqxp(wfwO iiiiiii,4 ++==
,4,3ifor),
y(O
or,2,1i
for),x(O
2i
i
Bi,1
Ai,1
==
==
==
i
i
i
i
ii
ii5w
fw
fwO
http://www.astro.oma.be/SIDChttp://www.astro.oma.be/SIDChttp://www.astro.oma.be/SIDC -
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We use rainfall data in Indonesia from NCEP
Reanalysis at
http://www.cdc.noaa.gov/cdc/data.ncep.reanalysis
and fuzzy c-means method with three seeding regions
for initial matrix fuzzy c-partition of three cluster centers i.e. :
ANFIS PREDICTION
0
50
100
150
200
1948
1952
1956
1960
1964
1968
1972
1976
1980
1984
1988
1992
1996
2000
2004
2008
2012
Years
NumbersSunspo
ANFIS Prediction Obs. Sunsspot
Figure 1. ANFIS prediction of sunspot numbertime series.
Bukittingi region for western Indonesia,, Jayapura
region for eastern Indonesia and Pontianak region for middle
Indonesia. This method is based on fuzzy set as partition
matrix for grouping a collection of n data set in to c classes, we
define object function for fuzzy as Euclidian distance. The
result of the clustering is shown in Figure 2. It is shown that
Jakarta region (Jabodetabek) is similar (0.6) to middle region
which is dominated by solar cycle, is similar (0.5) to western
region which is dominated by IOD cycle, and is similar (0.5) to
eastern region which is dominated by ENSO cycle. The result
of climate clustering in Indonesia is using the following
algorithm.
Fuzzy c-means Algorithm
1. Fix c (2c n) and select a value for parameter m,initialize the partition matrix U(0), each step in this
algorithm will labeled r, where r=0,1,2,..
2. Calculate the c centers {v i(r)} for each step.
3. Update the partition matrix forrth step, U (r) as follow:
=
=
=+
kIfor
m
c
j drjk
drikr
ik
1)1'/(2
1 )(
)()1(
(7)
4. If + )()1( rr UU ,stop; otherwise set r=r+1 and
return to step 2
5. Calculate the similarities of the c center :
=
== n
k
mik
n
k kjxm
ik
ijv
1
'
1
.'
(8)
Figure 2. Climate regions in Indonesia based on fuzzy clustering
IV.The Correlation of Sunspot Number to Rainfall in
Indonesia
With the equator crossing Indonesia, the sensible heat
flux plays an important role in global circulations. The latent
heat which originates mainly from the release of latent heat
when water vapor condenses into clouds droplets(a number of
large clouds form through convections in the Inter Tropical
Convergence Zone (ITCZ) which is above Indonesia). The cold
monsoon season in northern hemisphere (Asian monsoon) andin the southern hemisphere (Australian monsoon) are
influenced by the heat source distribution or the release of
latent heat above Asia and in the neighborhood regions. At
present it seems that the Indonesian zone holds the key to
southern oscillation system which determines the forcing of
Jaya Pura
0
100
200
300
400
Years
0
50
100
150
200
Avg precip sspot
Figure 3 Yearly precipitations in Jayapura region vs.
sunspot numbers.
http://www.cdc.noaa.gov/cdc/data.ncep.reanalysishttp://www.cdc.noaa.gov/cdc/data.ncep.reanalysis -
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Pontianak Region
Corre lation Sunspot vs Precip =0.88
0
100
200
Years
Sunspot/Pre
cip
-200
0
200
ave-sunspot ave-precip
Figure 4. Correlation between sunspot numbers and
yearly precipitation in Pontianak region.
El Nino Southern Oscillation (ENSO). Therefore,
Indonesia, through which the equator crosses, has the
maximum sensible heat flux, high rainfall, and monsoon
circulations. Consequently, it is one of the most primal zones
for convection processes, an equatorial-tropical zone where
Coriolis effects are practically nullified, where atmosphericcirculations are very different compared to the extra-tropical
zones.The observations and studies on Indonesian climate are
limited, and the mathematical formulations of tropical
dynamics are far more complex relative to those in the extra-
tropical zones. The distinct daily convection variability induced
by land-sea wind circulations over some islands in Indonesia
characterizes the aspect of rainfall throughout the Indonesian
Archipelago which are very different from other regions on the
earth. The studies mentioned above, show that rainfall is an
important quantity in the Indonesian Archipelago and sunspot
is believed to be the major predictor.
Using rainfall data in Indonesia from NCEP Reanalysis
http://www.cdc.noaa.gov/cdc/data.ncep.reanalysis
We can get links between sunspot numbers and rainfall,
although the correlations which existed in general are weak. In
other words, these signify that the dynamics of the atmosphere
is being viewed as the cause of the small correlations.
However, in the case of static model atmosphere, determination
of correlations based on data averaging of sunspot numbers on
yearly basis against the yearly rainfall for various regions in
Indonesia, one comes to time series as shown in Figures 3, 4
and 5 .
From Figure 3 we can conclude that eastern Indonesia
(Jayapura region) which represented Eastern Indonesian
Maritime Continent is strongly influenced by ENSO.
Jabodetabek
0
200
400
Years
mm/month
0
100
200
Avg Precip Avg-sspot
Figure 5. Maximum precipitation in Jabodetabek in
1968, 1981, 1992, 2002 correspond to sunspot number
maximum. Precipitation maximum in 1976, 1986, 1996,
and (2007) correspond to sunspot number minimum or
galactic cosmic ray maximum.
After 1976 sunspot numbers maximum SMax and
sunspot numbers minimum SMin correspond to precipitations
above normal also to La Nina and maximum eruptions ME or
CME corresponding to precipitations below normal and also toEl Nino.[4, 5] In Pontianak region which represent middle
Indonesian Maritime Continent, the yearly precipitation is
mainly determined by sunspot cycles (Figure 4). Precipitations
above normal occur at sunspot maximum SMax, and
precipitations below normal at sunspot minimum SMin.
Precipitations in east Indonesia which represent North
Australia Indonesian Monsoon are influenced by ENSO similar
to those observed in Jayapura region. (Figure 3) Precipitations
in Jakarta region or Jabodetabek are weakly influenced by
ENSO. The peaks of yearly precipitations correspond to the
peaks of sunspot numbers, but at the sunspot numbers
minimum which correspond to galactic comic ray maximum,
the yearly precipitations also maximum.(Figure 5).
The west Indonesian region is mainly influenced by IOD
that also correlated to solar cycle. [5]
The fuzzy c-means clustering shows that the western
Indonesian region is influenced mainly by IOD, the eastern
Indonesian region is influenced mainly by ENSO and the
middle region is mainly influenced by solar activity.
So, by knowing sunspot number time series as predicted
by ANFIS and fuzzy clustering of climate regions we can
predict the coming extreme weather for each regions in
Indonesia
REFERENCES[1] H. Svensmark, Cosmoclimatology : a new theory emerges. Astronomy &
Geophysics,Vol. 48, pp 1.18-1.24, 2007[2] T. Landscheidt, Solar Activity: A Dominant Factor in Climate Dynamics,
Schroeter Institute for Research in Cycles of Solar Activity,http://www.johndaly.com/solar/solar.htm, 1988.
[3] K.S. Carlslaw, R.G. Harrison, J. Kirkby, Cosmic Rays, Clouds, and
Climate, Sciences Compass, Vol. 298, 2002.
[4] T. Landscheidt, New ENSO Forecast Based on Solar Model, SchroeterInstitute for Research in Cycles of Solar Activity, 2003.
[5] The H. L., P. M. Siregar,Using System Dynamics of Ciliwung River to
Predict Floods, Workshop on Nonlinearity 2k6, IPB, Bogor, 2006.
[6] J.S.R.Jang, C.T. Sun, E. Mizutani, Neuro-Fuzzy and Soft Computing,Prentice Hall, Inc., 1997.
http://www.cdc.noaa.gov/cdc/data.ncep.reanalysishttp://www.cdc.noaa.gov/cdc/data.ncep.reanalysis -
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